Medium induced resolution enhancement for broadband imaging

Habib Ammari (1) , Josselin Garnier (2, 3) , Julien de Rosny (4) , Knut Solna (5)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LJLL - Laboratoire Jacques-Louis Lions
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 IL - Institut Langevin - Ondes et Images (UMR7587)
5 Department of Mathematics [Irvine]

A number of recent studies discuss the phenomenon of super resolution, that is, the fact that a target can be localized with higher resolution than half a wavelength as suggested by the classical diffraction limit. Here we discuss a special type of super resolution corresponding to a high contrast in wave speed at the location of respectively the point of observation and the one of the target. We quantify the resolution achieved in this case and discuss image stability. It turns out that the image is stable with respect to measurement noise but very sensitive to medium uncertainty. The signal-to-noise ratio can in fact be significantly enhanced by exploiting resonance frequencies and we discuss this in detail, considering source as well as reflector broadband imaging

Mots clés: imaging in complex media; super-resolution

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Habib Ammari, Josselin Garnier, Julien de Rosny, Knut Solna. Medium induced resolution enhancement for broadband imaging. Inverse Problems, 2014, 30 (8), pp.085006. ⟨hal-01108792⟩